Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×Dic25 |
| derived, Sylow | C25 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D25 |
| commutator, hypocenter | C25 | C2×C4×C8 |
| Frattini | C2×C4×C5 | C22×D5 |
| Fitting | C22×C8×C25 | C2 |
| socle, prime radical | C23×C5 | C4×D5 |
| cosocle | C2×C4×C25 | C23 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C22×C8 | |
243 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
448 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 726);